Show commands:
Magma
magma: G := TransitiveGroup(11, 7);
Group action invariants
| Degree $n$: | $11$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $7$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $A_{11}$ | ||
| CHM label: | $A11$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | yes | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,2,3), (3,4,5,6,7,8,9,10,11) | magma: Generators(G);
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Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Prime degree - none
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
| Label | Cycle Type | Size | Order | Representative |
| $ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $1$ | $1$ | $()$ | |
| $ 3, 3, 3, 1, 1 $ | $123200$ | $3$ | $( 1, 4, 6)( 2,10, 5)( 3, 7, 8)$ | |
| $ 9, 1, 1 $ | $2217600$ | $9$ | $( 1, 2, 8, 4,10, 3, 6, 5, 7)$ | |
| $ 3, 3, 1, 1, 1, 1, 1 $ | $18480$ | $3$ | $(1,4,5)(3,6,7)$ | |
| $ 5, 1, 1, 1, 1, 1, 1 $ | $11088$ | $5$ | $( 2, 8,10,11, 9)$ | |
| $ 5, 3, 3 $ | $443520$ | $15$ | $( 1, 5, 4)( 2,10, 9, 8,11)( 3, 7, 6)$ | |
| $ 2, 2, 1, 1, 1, 1, 1, 1, 1 $ | $990$ | $2$ | $( 2,11)( 9,10)$ | |
| $ 3, 1, 1, 1, 1, 1, 1, 1, 1 $ | $330$ | $3$ | $(3,6,7)$ | |
| $ 3, 2, 2, 1, 1, 1, 1 $ | $69300$ | $6$ | $( 2,11)( 3, 7, 6)( 9,10)$ | |
| $ 3, 3, 2, 2, 1 $ | $277200$ | $6$ | $( 1, 4, 5)( 2, 9)( 3, 6, 7)(10,11)$ | |
| $ 4, 2, 2, 2, 1 $ | $207900$ | $4$ | $( 1, 7)( 2,10, 9,11)( 3, 4)( 5, 6)$ | |
| $ 6, 4, 1 $ | $1663200$ | $12$ | $( 1, 3, 5, 7, 4, 6)( 2,11, 9,10)$ | |
| $ 2, 2, 2, 2, 1, 1, 1 $ | $17325$ | $2$ | $(1,7)(2,9)(3,4)(5,6)$ | |
| $ 6, 2, 1, 1, 1 $ | $554400$ | $6$ | $(1,3,5,7,4,6)(2,9)$ | |
| $ 4, 2, 1, 1, 1, 1, 1 $ | $41580$ | $4$ | $( 1, 5, 3, 6)( 2,11)$ | |
| $ 4, 3, 2, 1, 1 $ | $831600$ | $12$ | $( 1, 6, 3, 5)( 2,11)( 4, 8, 7)$ | |
| $ 4, 4, 1, 1, 1 $ | $207900$ | $4$ | $( 1, 8, 5, 4)( 2,10,11, 9)$ | |
| $ 3, 2, 2, 2, 2 $ | $34650$ | $6$ | $( 1, 5)( 2,11)( 3, 7, 6)( 4, 8)( 9,10)$ | |
| $ 4, 4, 3 $ | $415800$ | $12$ | $( 1, 4, 5, 8)( 2, 9,11,10)( 3, 6, 7)$ | |
| $ 8, 2, 1 $ | $2494800$ | $8$ | $( 1,10, 4, 2, 5, 9, 8,11)( 3, 6)$ | |
| $ 11 $ | $1814400$ | $11$ | $( 1, 4, 6,10, 5,11, 8, 2, 3, 9, 7)$ | |
| $ 11 $ | $1814400$ | $11$ | $( 1, 7, 9, 3, 2, 8,11, 5,10, 6, 4)$ | |
| $ 7, 1, 1, 1, 1 $ | $237600$ | $7$ | $( 1, 3,10, 5, 7, 2,11)$ | |
| $ 7, 3, 1 $ | $950400$ | $21$ | $( 1, 2, 5, 3,11, 7,10)( 6, 9, 8)$ | |
| $ 7, 3, 1 $ | $950400$ | $21$ | $( 1, 2, 5, 3,11, 7,10)( 6, 8, 9)$ | |
| $ 6, 3, 2 $ | $1108800$ | $6$ | $( 1, 6, 5,11, 9, 4)( 2, 8)( 3, 7,10)$ | |
| $ 5, 5, 1 $ | $798336$ | $5$ | $( 1, 3, 5, 6, 4)( 2,11, 8, 9,10)$ | |
| $ 5, 3, 1, 1, 1 $ | $443520$ | $15$ | $( 2, 9,11,10, 8)( 3, 7, 5)$ | |
| $ 7, 2, 2 $ | $712800$ | $14$ | $( 1, 3, 4, 9, 6, 2, 8)( 5, 7)(10,11)$ | |
| $ 5, 2, 2, 1, 1 $ | $498960$ | $10$ | $( 2, 8,10,11, 9)( 4, 5)( 6, 7)$ | |
| $ 5, 4, 2 $ | $997920$ | $20$ | $( 1, 3, 4, 6)( 2, 9,11,10, 8)( 5, 7)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $19958400=2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | magma: Order(G);
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| Cyclic: | no | magma: IsCyclic(G);
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| Abelian: | no | magma: IsAbelian(G);
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| Solvable: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 19958400.a | magma: IdentifyGroup(G);
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| Character table: | 31 x 31 character table |
magma: CharacterTable(G);